Comment by datsci_est_2015
11 hours ago
Not to mention physics, which is useful for understanding why things are the way they are. Which, is an important skill lest you fall into anti intellectual traps like flat earthism.
Calculus is a shared language in the grand universal ocean of intellectual cultural. Rejecting calculus is rejecting part of that culture…
Yeah, for me the real click was in AP Physics where we derived an equation for some motion property rather than just being handed the formula as I had been in, say, 8th grade science. The meta lesson is that you can use math to get more information out of a model than you think you have, which, yeah, keeps you from becoming a 5G get the facts style individual.
I loved learning about jerk, snap, crackle, and pop as higher-order derivatives of position wrt time in physics.
I’m not sure there’s enough overlap between physics and calculus to justify calculus. That might mean you can’t derive physical equations yourself, but no one needs that who isn’t becoming a physicist.
F=ma is slightly important for physics, no? And deriving the equations is kind of the point; it's the understanding of "why" something is true.
e.g. I can tell you things act like a spring near (stable) equilibrium, and you can believe me, but why on Earth would that be true? Well, Taylor expand the potential at equilibrium. Define V(0)=0, and equilibrium means V'(0)=0, so V(x) ~ V''(0)/2 x^2, so F = -dV/dx = -V''(0)x, which is a spring with spring constant k=V''(0).
That's all a very conceptual explanation; the point is near an equilibrium, zoom in and you have a parabolic potential! What is the potential for a spring? A parabola! This is basic Calc BC stuff, but it also justifies why we might care about about simple harmonic motion. Calculus is the whole business of "zooming in."
> I’m not sure there’s enough overlap between physics and calculus to justify calculus.
You need calculus to design a windmill or an auto engine or an electric motor beyond the "just sort of works" level. Most of analog electrical engineering is defined by calculus. Althogh, yes, you can get LTSPICE to do most of that for you.
I mean one example is like a dampened spring system or RLC circuits or something. You can simplify a lot of systems down to those types of simple physics systems you learn about in class.
A lot of it I think is just training people to adopt a "physics-like" or "math-like" way of thinking and giving them a general overview of how things work.